Immigration Minister Scott Morrison said the claims were unsubstantiated, and no investigation has been launched by Indonesian authorities.

But an Indonesian detective this afternoon said police were looking into the asylum seekers' allegations.

Local police from Kupang, where the asylum seekers were taken, say they have statements from the passengers.

Chief Detective Sam Kawengian says the claims warrant investigation and he has invited Australian authorities to travel to Kupang and view the evidence.

Detective Kawengian said that Australia is welcome to send officials to visit Kupang and review the physical evidence and the statements that have been taken for themselves. He hasn't said whether he wishes to interrogate Australian authorities or members of the Australian Navy or anything like that about the situation.

He added police have filed preliminary reports about what they have seen and been told by the asylum seekers.

Earlier today Mr Morrison said he would not tolerate people "sledging" Australian Navy personnel, and the claims of abuse were unsubstantiated.

"The Australian Government is not going to put up with people sledging the Australian Navy with unsubstantiated claims when they have high levels of motivation for spinning stories in order to undermine this government's very successful border protection program," he said.

"There has been no police investigation in Indonesia, there has been nothing of that sort."

Speaking to reporters in Sydney, Mr Morrison also attacked the ABC for broadcasting the claims.

"I think the mere publication of things that are clearly so unsubstantiated I think is very unfortunate," he said.

In an interview with Fairfax Radio, the minister repeated his concerns about the report.

"I want to address something pretty appalling that was being reported by the ABC this morning - airing unfounded, unsubstantiated, outrageous allegations against our Navy and our Customs and our border protection service," he said.

"I mean there [has] been no police investigation in Indonesia."

MP says Australia should guarantee safety

One Indonesian MP has told the ABC that Australia should guarantee the safety of all asylum seekers.

"The country of destination should protect them," MP and foreign affairs commission member Tantowi Yahya told 7.30.